This is a very post-hoc justification. It isn’t at all clear that the most accurate set of priors will actually do that. Note that for example, from a Kolmogorov standpoint, 3^^^^3 is pretty simple.
It’s not post-hoc at all. The more the number of people the mugger gives for X, the less significant $5 would be to him. This decreases the likelihood of the scenario that such a mugger would actually want to mug someone for a value that is so meaningless to him. This in turn means that given such a mugging, it is more likely that the mugger is a fake the larger X is.
Of course, you could argue that the mugger has some motive other than direct financial gain from the money (if he just wants to watch humans squirm, the insignificance of $5 doesn’t matter), but the same applies to all motives: watching a human squirm is less significant to a very powerful mugger than to a less powerful mugger, just like $5 is less significant to a very powerful mugger than to a less powerful mugger.
Furthermore, larger numbers for X are more beneficial for fake muggers than smaller numbers, when mugging utility maximizers. I should therefore expect the distribution of fake muggers to be more weighted towards high values of X than the distribution of real muggers (it is beneficial to some real muggers to increase X, but not to all of them). Again, the larger X is, the greater the chance the mugger is fake.
This is a very post-hoc justification. It isn’t at all clear that the most accurate set of priors will actually do that. Note that for example, from a Kolmogorov standpoint, 3^^^^3 is pretty simple.
It’s not post-hoc at all. The more the number of people the mugger gives for X, the less significant $5 would be to him. This decreases the likelihood of the scenario that such a mugger would actually want to mug someone for a value that is so meaningless to him. This in turn means that given such a mugging, it is more likely that the mugger is a fake the larger X is.
Of course, you could argue that the mugger has some motive other than direct financial gain from the money (if he just wants to watch humans squirm, the insignificance of $5 doesn’t matter), but the same applies to all motives: watching a human squirm is less significant to a very powerful mugger than to a less powerful mugger, just like $5 is less significant to a very powerful mugger than to a less powerful mugger.
Furthermore, larger numbers for X are more beneficial for fake muggers than smaller numbers, when mugging utility maximizers. I should therefore expect the distribution of fake muggers to be more weighted towards high values of X than the distribution of real muggers (it is beneficial to some real muggers to increase X, but not to all of them). Again, the larger X is, the greater the chance the mugger is fake.